Beyond Natural Sciences
Applied Mathematics and Nonlinear Sciences

Article details
Buy now
Available online: February 27, 2018

Perfect phase-coded pulse trains generated by Talbot effect

Carlos Férnandez-Pousa
Volume 3 - Issue 1.     Year 2018.     Pages 23–32.

DOI: 10.21042/AMNS.2018.1.00003

Abstract

A perfect phase sequence is a finite and ordered set of constant-amplitude complex numbers whose periodic autocorrelation vanishes at any non-zero time shift. They find multiple applications in science an engineering as phase-coded waveforms, where the sequence defines the relative phases within a burst of electromagnetic or acoustic pulses. We show how a physical propagation effect, the so-called fractional Talbot phenomenon, can be used to generate pulse trains coded according to these sequences. The mathematical description of this effect is first reviewed and extended, showing its close relationship with Gauss perfect phase sequences. It is subsequently shown how it leads to a construction of Popovic's Generalized Chirp-Like (GCL). Essentially, a set of seed pulses with prescribed amplitude and phase levels, cyclically feeds a linear and dispersive medium. At particular values of the propagation length, multiple pulse-to-pulse interference induced by dispersion passively creates the sought-for pulse trains composed of GCL sequences, with the additional property that its repetition rate has been increased with respect to the seed pulses. This observation constitutes a novel representation of GCL sequences as the result of dispersive propagation of a seed sequence, and a new route for the practical implementation of perfect phase-coded pulse waveforms using Talbot effect.

   View all volumes & issues

Journal details

ISSN:
2444-8656
Category:
Applied Mathematics, Nonlinear Sciences

Metrics

This journal is indexed by:

This journal works looking for quality under the standards of:

© UP4, Institute of Sciences, S.L.

CIF: B-30894240
C/ Isla de la Bahía, no8, BQ 3, 4, VVDA 70,
FINCA 06813, 30868 Isla Plana (Cartagena)
(+34) 968 152055/ (+34) 600397005
info@up4sciences.org
http://www.up4sciences.org

Blog

  
Society registered at the Region of Murcia Mercantil Register issue 3111, paper 84, inscription 1 with sheet MU-88065